Entanglement growth in diffusive systems

Žnidarič, Marko (author)

Entanglement helps in understanding diverse phenomena, going from quantifying complexity to classifying phases of matter. Here we study the influence of conservation laws on entanglement growth. Focusing on systems with U(1) symmetry, i.e., conservation of charge or magnetization, that exhibits diffusive dynamics, we theoretically predict the growth of entanglement, as quantified by the Rényi entropy, in lattice systems in any spatial dimension d and for any local Hilbert space dimension q (qudits). We find that the growth depends both on d and q, and is in generic case first linear in time, similarly as for systems without any conservation laws. Exception to this rule are chains of 2-level systems where the dependence is a square-root of time at all times. Predictions are numerically verified by simulations of diffusive Clifford circuits with upto ~ 10$^5$ qubits. Such efficiently simulable circuits should be a useful tool for other many-body problems.

• Language: English
• Keywords: quantum mechanics, entanglement, statistical mechanics, condensed matter physics
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2020
• Number of pages: 9 str.
• Numbering: Vol. 3, art. 100
• PID: 20.500.12556/RUL-128559
• UDC: 530.145
• ISSN on article: 2399-3650
• DOI: 10.1038/s42005-020-0366-7
• COBISS.SI-ID: 17689859
• Publication date in RUL: 19.07.2021

Record is a part of a journal

• Title: Communications physics
• Shortened title: Commun. phys.
• Publisher: Springer Nature
• ISSN: 2399-3650
• COBISS.SI-ID: 2048602387

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
• Licensing start date: 01.06.2020

Secondary language

• Language: Slovenian
• Keywords: kvantna mehanika, prepletenost, statistična mehanika, fizika kondenzirane snovi

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: J1-1698
• Name: Načrtovanje večdelčnega transporta

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0402
• Name: Matematična fizika